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I'm currently interested in divergent series, especially as studied from a complexanalytic point of view. Resummation, constructed in the right way, provides a strictly stronger alternative to analytical continuation hence it may be deemed as a type of generalized analytical continuation. The goal is to develop this generalized analytical continuation enough to start being able to analyze the many fascinating functions out there that analytical continuation can't illuminate (for instance, Gottfried's Tetaeta series $\sum (1)^n n^{n^x}$, Jacobi's Theta functions, the Prime Zeta function, etc.)
I am a sophomore college student, so all of my questions are rather straightforward.
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